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tahayassen
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We learned about those functions last semester but they seemed to have to do nothing with sine and cosine? They were defined using the exponential function.
That Neuron said:Which is just simple differentiation and d/dx(Coshx) = -Sinhx, in this way Coshx and Sinhx follow the same cycling pattern of differentiation as coax and sins.
bluesky20 said:solve: z=Asin(2πft+α) where A=0.06,α=58degree
The names sinh and cosh come from the abbreviations of the Latin words "sinus hyperbolicus" and "cosinus hyperbolicus", which translate to "hyperbolic sine" and "hyperbolic cosine" in English.
The hyperbolic sine and cosine functions were named after sinusoidal functions because of their similarities in shape and properties. Just like how the sine and cosine functions are used to describe circular motion, the sinh and cosh functions are used to describe hyperbolic motion.
The terms sinh and cosh were first introduced by mathematician Vincenzo Riccati in the 18th century. However, the concepts of hyperbolic functions can be traced back to earlier mathematicians such as Johann Heinrich Lambert and Leonhard Euler.
The relationship between sinh and cosh is similar to that of sine and cosine. Just like how sine and cosine are related by the Pythagorean identity, sinh and cosh are related by the hyperbolic Pythagorean identity: cosh2(x) - sinh2(x) = 1.
Sinh and cosh have many applications in mathematics, physics, and engineering. They are used to solve differential equations, describe hyperbolic geometry, and model physical phenomena such as heat transfer and electrical circuits. They are also closely related to other important mathematical functions, such as the exponential and logarithmic functions.